Saturday, February 24, 2007

Leo Sweeney, SJ, on Infinity

"Lawrence Gage" (the erstwhile Meta-Jester) has recently posted an excellent piece on the philosophical concept of infinity, and when I mentioned Leo Sweeney's work on the subject, Professor Gage asked me to say a bit more about what that theory was. Posting something about Sweeney is something that I have been meaning to do for a long time, and with the current incentive coming in the form of a reasonable request from a fellow-traveler in the Ivy League, I wouldn't be worth the name "Crimson Catholic" if I left this for later. So here is my attempt to fill out Professor Gage's post with some information from Leo Sweeney, SJ, Divine Infinity in Greek and Medieval Thought (NY: Peter Lang Publishing Co., 1998).

Sweeney summarizes the implications of Aristotle's concept of infinity as follows (p. 6):
"For Aristotle, then, infinity basically is associated with quantity and is synonymous with imperfection. This synonymity has two important consequences. The Greek philosopher cannot predicate it directly of God Himself (the First Mover and primal Separate Intelligence), but only of His power, and this through an extrinsic predication. [As one might guess, Fr. Sweeney uses this term to refer to descriptions of God as related to other entities rather than God's own being -- JP.] That is, His power is so perfect as to be the cause of an infinite effect, viz., the endlessly recurring circular motion of the heavenly bodies through an infinity of time; it is this motion alone to which infinity directly belongs and through which divine power receives the predication (Meta. 1073a6-10). Secondly, the material universe cannot be actually infinite in extent, nor is it merely one of an infinite number of universes, since such sort of actual infinites are contradictory and impossible. Moreover, it is finite in virtue of the fact that as "universe" it is whole, all-inclusive, complete, and perfect; and whatever is whole, complete, and perfect has an end, which is its limit and termination (Phys. 207a7-14)."

The next stage in development is the concept of Plotinus. Plotinus does not explicitly break the identification between infinity and imperfection so as to render "infinite" a proper predicate for God, but he does implicitly allow such predication in saying that God is "beyond being." Because of this status, infinity is not pejorative with respect to God because He is not the sort of entity in which the absence of limits is a deficiency. Sweeney (p. 7) explains the situation as follows:
"Infinity as Perfection. Unlike Aristotle, though, Plotinus developed a theory of infinity that is synonymous with perfection and that is applicable to God Himself. This theory rests on the insight that form and being are determining and terminating factors wherever found ([Enneads] If something is without form and being, it is without their determination and, this, is indeterminate or infinite. If it should possess them but does not, that status of indetermination is coterminous with imperfection. Thus, matter of itself is below form and entity and, accordingly, is indeterminate and simultaneously imperfect (;;;; On the other hand (and of this Aristotle shows no explicit awareness), God rises above the being and form proper only to the lower levels of reality, viz., the intelligible, psychical, and sensible universes, and thereby also transcends any formal determinations. By this transcendence He is infinite, and such infinity is aligned with absolute perfection and actual excellence.... (; see also;;;

Infinity and Nonbeing. In thus showing that inifinity can be coextensive with perfection and thereby predicable of the divine reality itself, Plotinus made a major contribution to the development of the concept of infinity. But one must remember that this predication is only implicit in Plotinus' text."

In Plotinus, we have at least an implicit metaphysical concept of a real infinity contrary to Aristotle. A similar explicit account based on the Neoplatonic concept of participation is articulated by Gregory of Nyssa; God is infinite in that he does not have His perfections by participation in any other entity (see p. xv and also Sweeney's "Augustine and Gregory of Nyssa: Is the Triune God Infinite in Being?" in Roland Teske et al. (eds.), Collectanea Augustiniana (vol. 2): Presbyter Factus Sum (NY/Bern: Peter Lang Publishing Co., 1992), 321-26). One might refer to this as the Neoplatonic concept of real infinity. It appears to be followed not only by Gregory Nyssen (who also employs what Sweeney calls a "homespun" anticipation of St. Thomas's later idea, but without the explicit concepts of act and potency) but also by Pseudo-Dionysius, John Damascene, and John Scotus Eriugena (p. 9). I would add St. Maximos Confessor per Eric D. Perl's 1992 dissertation at Yale: "Methexis: Creation, Incarnation, and Deification in St. Maximus"). The bottom line is that there was a metaphysical distinction (although not the same as St. Thomas's) introduced to avoid Aristotle's conclusion about infinity being predicated of a real entity.

In the West, this distinction was more or less unknown, and St. Augustine's teaching on the subject was not detailed or rigorous (summarized well in Sweeney's article in Presbyter Factus Sum, to which I will refer the interested reader in the interest of keeping this post more focused on its topic). Acccordingly, the predicate "infinite" was frequently treated according to the example of Aristotle of Boethius as being only improperly predicated of divinity and properly only of the infinite motion God produces (Sweeney cites numerous examples on p. 9). It wasn't until Bonaventure and Aquinas that the philosophical problem was studied in detail, and this was the point at which St. Thomas's famous notion of God as unmixed with either matter or potency (subsistent being) was used to resolve the problem. Sweeney says the following of Aquinas and Bonaventure (p. 16):
"[T]hey broke with Aristotle by predicating infinity of God Himself, as Plotinus also had. Yet their positions significantly differ from the Neoplatonist's because especially Aquinas' rests upon an obviously different metaphysics (see below, ch. 19).

For example, Aquinas agreed with Plotinus that forms and, in general, every sort of act are determining factors for whatever receives them. Accordingly, a recipient such as matter is indeterminate and infinite (and also imperfect) when considered in itself and as lacking form. But in contrast to Plotinus, Thomas taught also that matter and all other types of potencies are not mere negations, privations, or mental constructs, but are genuinely real and actually existing components within existents and cause their own sort of determination. Accordingly, a subsistent form or act is without the limiting determination of matter or of potency and, thus, is infinite and infinitely perfect."

Given the novel concept of potency that St. Thomas introduces, which recognizes the difference between existence and essence, I think Zellini has erred in his understanding of St. Thomas's infinity "on the part of matter." St. Thomas would certainly say the limiting determination of matter and potency is an imperfection in an entity's act of being (perhaps "mode of existence" would be a helpful synonym), but at the same time, it is a true part of that act. This is not the same as Aristotle's view (or Boethius's), which neglects the distinction between essence and existence based on the same confusion between form and matter that Prof. Gage identified. Viewed in this way, I do not think that Descartes has departed from the Schoolmen in anything other than terms, as Fr. Sweeney points out (p. 11): "R. Descartes thought that only God should be called 'infinite,' whereas quantitative itsems should be termed 'indefinite' (see Reply to Obj. 1, 2:17; Principles of Philosophy, 1.14, 26, 27)." As further evidence that the doctrine of potency is at the heart of what St. Thomas's means by infinity "on the part of matter," I would note that the controversy with Duns Scotus on this topic (Sweeney, p.553-558) seems to clearly turn on Scotus's confusion about St. Thomas's doctrine of potency.

As I said, I think that Prof. Gage has actually identified the conceptual problem in Aristotle correctly, but I don't believe that Zellini has taken the full implications of that distinction into account in concluding that Descartes was an innovator. It seems to me that the metaphysical roots of Descartes's idea were well in place in St. Thomas. While one can't really deny that "Where previously it was assumed that the essence of mathematical infinity lay in quantity and variability, now the concepts of order and multiplicity are basic" (Sweeney, p. 12), the general direction away from Aristotle appears to have been the work of St. Thomas, perhaps taking some conceptual inspiration from the work of Richard Fishacre (though likely not much earlier than that for the explicit concept; see Francis Catania, "Albert the Great on Divine Infinity: A Reply to Francis Kovach" in Greek & Medieval Studies in Honor of Leo Sweeney, S.J., William J. Carroll & John J. Furlong, eds. (NY: Peter Lang Publishing, Inc., 1994)). I'm always wary of giving the Enlightenment and modernity credit for "innovations" that really owed their concepts to Scholastic thought (as is often done with empiriological science), and this seems to be another example where the Schoolmen beat the Enlightenment to the punch.

Tuesday, February 20, 2007

The art of the vacuous concept

Some people can't seem to understand that it doesn't suffice to say "I believe X," where X is a conceptual nonentity. It reminds me of Nestorius: "No, I don't believe that Christ is two persons; I believe that he is the prosopon of the union." Same things happening here: "I believe torture is intrinsically evil, but I believe that you determine the desperation of the situation on a case-by-case basis" or "the key here for me when determining the porportionality is the extremity of the situation, which as a practical matter has to be worked out according to a case-by-case basis." Another example, to show I am not simply a blatant partisan, would be "The definition [of torture] should point to something that is intrinsically evil" conjoined with "The sin of torture consists in the disproportionate infliction of pain" (see also "more pain than was necessary"; "necessary" for what exactly?).

Mark Shea has been right from DAY ONE on this subject. The term "torture" in VS and GS must mean SOMETHING that cannot be done under any circumstances, and his opponents have offered definitions that are, in fact, conceptually vacuous (and note, pace Fr. Harrison, that Shea never said that deliberate infliction of pain, even severe bodily pain, was intrinsically evil, only that there must clearly be some cases that are). And Shea is entirely right to demand that someone who claims to answer him articulate some sort of meaningful counter-position, either by finding a clear paradigm case for the method of casuistry (which appears to be Shea's preference) or by articulating a clear moral principle (Zippy's preference), even if, as Fr. Harrison asserts, the question of the infliction of severe bodily pain as a method of interrogation is in some sense still open.

Contrary to the numerous "oh, poor me!" assertions that have been made about Shea's failure of understanding or imagination, he isn't obliged to believe nonsense or to protect the feelings of those who have chosen to believe it. And that's all the aptly-named Coalition for Fog appears to have: nonsense. It is not charity to allow people who to mistakenly cling to nonsense as if it actually meant something (which billions of people, many of them quite intelligent, have done throughout history and will no doubt continue to do). The example of Nestorius alone should suffice as a glaring example of just how far adherence to a vacuous concept can go.

If there has been an error on Mark Shea's part (and I think it is an error, not a lie), it has been to posit that there is some real political motivation behind this. I doubt that is the case. It seems to follow the pattern of Nestorius: one makes a major mistake early, and then spends the rest of the time trying to convince himself that he was too smart to have made such an obvious mistake. I'm just amazed by the demand for "accurate representation" by people who publicly state their own position in terms of absolutely meaningless circumlocutions like "the desperation of the situation," "case-by-case" or "the extremity of the circumstances," as if the mere utterance gives them conceptual content.

It's all the more incredible from people who then accuse Shea of being too vague, as in "Using the term 'terror suspect' is far too vague because we have no idea what the individual in question is suspected of doing. Are they a cell leader? A bombmaker? A chemical weapons expert? A member of the al-Qaeda ruling council?" What on earth does what the person is suspected of doing or who the person is have anything to do with anything? They won't even articulate why it is that these factors have anything to do with it. One could just as easily say "What is the person wearing? Does he have a green bandana or a red one?" Absent some link to the moral act in question (and this is that "object" issue that Zippy keeps harping on), these are all mere circumstances that cannot justify an intrinsic evil. (Incidentally, Jimmy Akin's justification that "there is no other, less painful way to save lives" is equally poor, as there is no intrinsic link between the act of torture and the information that is used to save lives.)

The fact that torture happens to get information out of people is morally irrelevant unless you can explain why it is that torture produces information so as to morally justify its use. Is it like the case of threatening to kill a child, so that the instinctive and natural horror at such a depraved and perverted act produces a natural response to avoid it, in which case torture produces information only by a grossly unnatural and immoral mechanism? Sure seems like it to me. But this sort of moral analysis, the very thing that would be required to give these sorts of definitions any sort of coherent conceptual content, is utterly absent. And that is ultimately where the F in CfF comes from. They are throwing mere words out there without doing the work to give them substance, and then complaining when somebody points out that their "position" is nothing but mist and shadow. I find it extraordinarily frustrating that someone resorts to "it's an open question" as a defense without bothering to formulate a tight, logical justification for that position. You're obliged to morally justify the acts you take or formally endorse whether or not the Magisterium has spoken on a subject, so you can't get away with saying "well, it's an open question, so no Catholic can tell me I'm wrong."

Consequently, I will have to respectfully dissent from my friends Dave Armstrong and Diane Kamer on this one. It is entirely possible for someone to say "I mean X and not Y," where X refers to some vacuous concept. That's more or less what Nestorianism was, so it's hard to say that someone can't honestly believe in nonsense. People have to be pushed not just to SAY that they don't have a certain belief but to explain WHY they don't have that belief. It's perfectly right to say "well, you say you believe X, but X is nonsense, so you really believe Y." Incidentally, I think that this has produced an inordinate amount of friction in Catholic/Orthodox debates, and we (on both sides) need to start moving past the "well, I said I didn't believe that, so you can't say that I do" position and get to a point where we can objectively demonstrate that apparent contradictions are not, in fact, contradictions. And that is what the CfF has consistently failed to do.